Modi, who swept to power in a general election last month, has accepted an invitation from Obama for two-way talks in Washington, the reports said.
No comment was immediately available from the Indian government press office or from the U.S. embassy.
Both countries are keen to boost security and economic ties - the Obama administration has set a goal of quintupling annual trade to $500 billion.
Scheduling has still to be finalised, but the summit would represent an upgrade from earlier expectations that Modi, 63, would meet Obama on the sidelines of the annual United Nations general assembly in New York.
Modi, a former chief minister of Gujarat, had been refused a U.S. visa over sectarian strife in the state in 2002, in which more than 1,000 people, mainly Muslims, were killed. He has denied any wrongdoing and an Indian Supreme Court inquiry found no case to answer.
The U.S. ambassador to India met Modi earlier this year, as opinion polls showed his Bharatiya Janata Party (BJP) on course for an election victory. U.S. officials had said a visa and an invitation to meet would probably be forthcoming if Modi won.
Modi wants to cautiously open up the Indian economy to foreign investment to boost growth and job creation.
His government may announce as soon as next month that it will allow foreign online retailers to sell their own products in India, creating a major business opportunity for players such as Amazon.